CALCULATING THE CAR’S PERFOMANCE
Having defined the main forces acting on the car, the performance can be calculated.
By vector addition of the forces trying to drive the car forward and hold it back we obtain
the resultant force acting in the direction of motion. This may be a positive force
accelerating the car or a negative force decelerating the car.
This force is used in conjunction with the Newtonian Mechanics formulas to calculate the
cars acceleration, velocity and distance travelled after a specified time. Remember the
force acting varies with car velocity and position on the track, while the formulas used
here assume the force is constant over the time interval chosen. Consequently our
calculated results will be inaccurate, as the forces acting on the car are constantly
changing, but for a short time interval the changes will be very slight. The inaccuracy
will increase the longer the time interval used. We have chosen a short time interval of
0.05 seconds so reasonable accuracy is achieved.
At the end of each time interval the forces acting on the car are re-evaluated and used to
calculate the performance for the next time interval. This iterative process is continued
until the car has travelled the track length.
THE CALCULATIONS
The following method is used to calculate the car’s performance.
1 DETERMINE THE RESULTANT FORCE ACTING ON THE CAR
Resultant force = Gravity + Air drag + Motor drive force + Rolling resistance
(the gravity force is the component acting up or down the hill see FIG 2)
NOTE: Standard Newtonian mechanics formulas are now used to calculate accelerations,
velocities and distances travelled. Refer to standard texts for derivations and full
explanations of their use.
2 CALCULATE THE ACCELERATION OF THE CAR
From Force (Newtons) = Mass (kg) × Acceleration (m/s²)
Transforming this we get
Acceleration = Force / Mass
3 CALCULATE THE DISTANCE TRAVELLED
( This is the distance travelled in the time interval.)
We now substitute the acceleration calculated into the formula for distance travelled.
Distance travelled = Initial velocity × Time + 0.5 × Acceleration × Time²